By far the simplest way to do this is to install VNC Server on the Desktop machine.

Then you can do the following from your laptop with RealVNC Viewer installed:
vncviewer desktop:1 -via user@servername.domain.com

To connect directly to the desktop. This will automatically SSH to servername.domain.com, forward a port to the destination VNC server, then connect to that port.
Replace desktop with the internal DNS name or IP of the desktop, and of course the rest should be obvious there.

As an alternative there's also X forwarding, which you can bounce through a tunnel, but XLib does not make any attempts to optimize for bandwidth.